Space of modular forms of level 3136, weight 1, and Character 3136.bm

• Label: 3136.1.bm
• Level: $3136$
• Weight: $1$
• Character orbit: 3136.bm
• Rep. character: $\chi_{3136}(99,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $448$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3136 = 2^{6} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3136.bm (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 64 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(448\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3136, [\chi])\).

	Total	New	Old
Modular forms	72	48	24
Cusp forms	8	8	0
Eisenstein series	64	40	24

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3136, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3136.1.bm.a	$3136$	$1$	3136.bm	64.j	$16$	$8$	$1$	$1.565$	\(\Q(\zeta_{16})\)	$D_{16}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}-\zeta_{16}q^{8}-\zeta_{16}q^{9}+\cdots\)